Excitonic effects in time-dependent density functional theory from zeros of the density response

TL;DR

This paper explores the analytic structure of dynamical exchange-correlation kernels in TDDFT, revealing how their poles relate to excitonic effects and enabling the development of simplified, accurate kernels for optical spectra calculations.

Contribution

It introduces a method to analyze the poles of xc kernels to better understand excitonic effects and proposes simple approximations that improve TDDFT spectral predictions.

Findings

Kernels' poles correspond to collective excitations.

Proposed kernels accurately reproduce excitonic features.

Method enhances efficiency of real-time TDDFT calculations.

Abstract

We show that the analytic structure of the dynamical xc kernels of semiconductors and insulators can be sensed in terms of its poles which mark physically relevant frequencies of the system where the counter-phase motion of discrete collective excitations occurs: if excited, the collective modes counterbalance each other, making the system to exhibit none at all or extremely weak density response. This property can be employed to construct simple and practically relevant approximations of the dynamical xc kernel for time-dependent density functional theory (TDDFT). Such kernels have simple analytic structure, are able to reproduce dominant excitonic features of the absorption spectra of monolayer semiconductors and bulk solids, and promise high potential for future uses in efficient real-time calculations with TDDFT.